CN107765347B - Short-term wind speed prediction method based on Gaussian process regression and particle filtering - Google Patents
Short-term wind speed prediction method based on Gaussian process regression and particle filtering Download PDFInfo
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Abstract
The invention discloses a short-term wind speed prediction method based on Gaussian process regression and particle filtering, which realizes online dynamic detection and correction of abnormal values and improves wind speed prediction precision. Firstly, determining an input variable set with the maximum correlation with a wind speed value at a time to be predicted by adopting a partial autocorrelation function, determining a state vector and constructing a proper training sample set, establishing a Gaussian process regression short-term wind speed prediction model in the training sample set, and giving a training process fitting residual error; then, establishing a particle filter state space equation by combining the state vector and a Gaussian process regression model, and performing state estimation on the current measurement value by adopting a particle filter algorithm; and finally, analyzing the estimated value and the residual error of the measured value of the particle filter, and judging and correcting the abnormal value according to the 3 sigma principle. The method provided by the invention can effectively detect and correct the abnormal value, improves the short-term wind speed prediction precision, and can better solve the problem of wind speed prediction of the power system.
Description
Technical Field
The invention relates to a method for predicting short-term wind speed of an electric power system, which predicts the wind speed of the electric power system and belongs to the technical field of electric power systems.
Background
At present, two methods of numerical weather forecast and statistical model are mainly used for wind speed prediction. The numerical weather forecast needs to establish a physical model, and information such as wind speed, wind direction, temperature and humidity is obtained through a micro-meteorology theory and computational fluid mechanics. The statistical model method mainly adopts the thought of mathematical statistics and carries out prediction by mining the internal rules existing among data. Such methods are mainly time-series, neural networks, support vector machines, kalman filtering, and the like. Since wind speed has typical characteristics of nonlinearity, strong fluctuation and strong randomness, a linear model based on time series analysis has difficulty in describing the wind speed variation characteristics. A short-term wind speed prediction model based on the BP neural network has good prediction accuracy, but the process is based on the 'black box' principle, and explicit mathematical expression is difficult to establish. A Support Vector Machine (SVM) model adopts structure risk minimization to replace experience risk minimization of a neural network, so that the SVM model has better generalization capability and is suitable for processing problems of small samples, high dimension and nonlinear regression, but the model has long time consumption in a hyper-parameter training process, and the wide application of the SVM model is limited to a certain extent. The ideal prediction precision is obtained through a Kalman wind speed prediction model established through time series analysis. However, the kalman filtering method is suitable for a linear mathematical model and has weak processing capability for a nonlinear process. The output of the Gaussian Process Regression (GPR) has the characteristic of probability distribution, and the GPR has better prediction precision compared with the SVM and BP neural network models. Therefore, the invention builds a GPR-based short-term wind speed prediction model.
Meanwhile, short-term wind speed prediction often has two important problems: 1) noise mixed with the historical wind speed sequence influences the accuracy of the prediction model. The wind speed sequence is inevitably influenced by various noise factors in the processes of acquisition, transmission, storage and the like, such as acquisition errors of measuring equipment, data loss in the data transmission process and the like. When the prediction model is trained, the abnormal values cause the predicted values to deviate from the true values, and the prediction result is difficult to give even under the severe condition of data loss. Meanwhile, inaccurate estimation of model parameters also reduces prediction accuracy. Statistical methods indicate that: in the training process, the sample points with the fitting values far deviating from the true values are abnormal value points. Thus, an abnormal value detection method based on the deviation is generated. The method mainly comprises the following steps: firstly, a mathematical model is established by using known data, and whether the data are abnormal or not is judged according to the residual error between the fitting data and the true value. The assumption is that fitting the residuals follows a gaussian distribution with a mean of zero. 2) Due to the hysteresis of the mechanism of the statistical model method, the change trend of the predicted value lags behind the true value of the wind speed, and particularly at the moment of sudden change of the wind speed, the output value of the predictive model is difficult to reflect the true value and the predicted value needs to be corrected.
Aiming at the first problem in the wind speed prediction process, the invention adopts an abnormal value detection method based on deviation. In the process of fitting the real value by using the GPR, the fitted value and the real value have larger deviation due to strong randomness and uncertainty of wind speed and hysteresis of a prediction model, so that the deviation at the position of the abnormal value is submerged, and the abnormal value is difficult to detect or causes false detection and missing detection. In order to eliminate larger deviation at a normal value, a nonlinear non-Gaussian filtering method, namely Particle Filter (PF), is introduced, so that a short-term wind speed prediction model based on combination of Gaussian process regression and particle filter (GPR-PF) is provided, and online dynamic detection and correction of an abnormal value are realized. The method can effectively detect and correct the abnormal value through the example verification.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problem that noise or data loss in a historical wind speed sequence affects wind speed prediction accuracy, the invention provides a short-term wind speed prediction method based on Gaussian process regression and particle filtering, which realizes online dynamic detection and correction of abnormal values, thereby accurately estimating model parameters and improving wind speed prediction accuracy. In order to effectively select an input variable set with larger correlation with the wind speed value at the moment to be predicted, the method measures the correlation between two variables by adopting a partial autocorrelation function, determines a training sample set and further determines a state vector. Establishing a state space equation through Gaussian process regression in a training sample set, carrying out state estimation on a current measurement value by adopting a particle filter algorithm, analyzing a residual error between an estimation value and the measurement value, and judging an abnormal value according to a '3 sigma' principle. And then correcting the abnormal value, and reestablishing a Gaussian process regression prediction model for the cleaned wind speed sequence. When wind speed prediction is carried out 15 minutes ahead, the state estimation is carried out on the latest measurement value by adopting a particle filter algorithm, and the online detection and correction of the abnormal value are realized. Finally, the example analysis result shows that the particle filter algorithm can effectively detect the abnormal wind speed value, and the wind speed prediction error is reduced.
The technical scheme is as follows: a short-term wind speed prediction method based on Gaussian process regression and particle filtering comprises the following steps:
1) acquiring basic data required by short-term wind speed prediction of a power system, and carrying out zero-averaging processing on the original data;
(2) determining an input variable set with the maximum correlation with the wind speed value at the moment to be predicted by adopting a partial autocorrelation function, determining a state vector and constructing a proper training sample set;
(3) establishing a Gaussian process regression short-term wind speed prediction model in a training sample set, and giving a training process fitting residual error;
(4) establishing a particle filter state space equation by combining the state vector and a Gaussian process regression model, and performing state estimation on the current measurement value by adopting a particle filter algorithm;
(5) analyzing the estimated value and the residual error of the measured value of the particle filter, and judging and correcting an abnormal value according to a '3 sigma' principle;
(6) and re-establishing a Gaussian process regression prediction model for the cleaned wind speed sequence. When wind speed prediction is carried out 15 minutes ahead, state estimation is carried out on the latest measurement value by adopting a particle filter algorithm, and online detection and correction of abnormal values are realized.
Further, in the step (1), zero averaging processing is performed on the original wind speed time series, wherein the zero averaging formula is as follows:
in the formula: x (t) is the time series of the original wind speeds,
is the average value of the sequence x (t).
Further, step (2) adopts a partial autocorrelation function to determine an input variable set with the maximum correlation with the wind speed value at the time to be predicted, and determines a state vector and constructs a proper training sample set, wherein the calculation method of the partial autocorrelation function comprises the following steps:
3.1 hypothesis xiIs an output variable, and when the lag order is k, the value of the partial autocorrelation coefficient is in a 95% confidence interval
Inner, then xi-kCan be used as one of the input vectors, if all the partial autocorrelation coefficient values are within the 95% confidence interval, then x is considered to bei-1Is an input variable;
3.2 for time series { x1,x2,L,xnThe covariance of lag order k is defined as gammak(γ is a variance when k is 0), the calculation formula is as follows:
in the formula: k is 0,1,2, L, M,
is the mean of the time series; m-n/4 is the maximum hysteresis order;
3.3 autocorrelation function (ACF) with a lag order of k is defined as ρk：
In the formula:
the covariance when the hysteresis order k is 0.
The PACF for a lag order of k is defined as αkk：
In the formula: k is 1,2, L, M.
Further, in the step (3), a Gaussian process regression short-term wind speed prediction model is established in the training sample set, and a training process fitting residual error is given, wherein the Gaussian process regression model prediction process is as follows:
4.1 assume that the training sample set is D { (x)i,yi) 1,2,3, ·, n } (X, y), wherein: x is the number ofi∈RmFor an m-dimensional input vector, the m × n-dimensional input matrix can be expressed as X ═ X1,x2,···,xn]N denotes the number of training sample points, yiE R is corresponding to xiAn output scalar of (1);
4.2 define the function space f (x) ═ Φ (x)Tω，f(x(1))、f(x(2))、…、f(x(n)) Forming a set of random variables and following a joint gaussian distribution, the gaussian process model can be expressed as:
in the formula: the mean obeying value of the independent white Gaussian noise is 0, and the variance is sigma2Is recorded as ε: N (0, σ)2)；δijIs a Kronecker delta function, when i is equal to j, the function delta ij1 is ═ 1; m (x) is a mean function of a finite dimension distribution family, and describes a wind speed mean output result; k (x, x') is a covariance function and describes the size of the wind speed variance;
4.3GPR prediction model establishes prior distributions in n-dimensional training set D, n*Dimension test set D*＝{(xi,yi)|i＝n+1,L,n+n*Down-converting into posterior distribution, training sample observation value y and output vector f of test data*Form a joint Gaussian distribution
Wherein K (X, X) ═ KnRepresenting an NxN kernel matrix of which element Kij＝k(xi,xj)；K(X,X*)＝K(X*,X)TFor testing dataX*A covariance matrix with the input X of the training set; k (X)*,X*) Is X*(ii) its own covariance;
4.4 deriving therefrom the predicted value f*The posterior distribution is
Wherein
Mean vector
The mean of the GPR model wind speed predictions, corresponding to the point prediction outputs,
to correspond to
Thereby obtaining the wind speed interval prediction result with the meaning of probability distribution.
Further, in the step (4), a state vector and a Gaussian process regression model are combined, a particle filter state space equation is established, and a particle filter algorithm is adopted to carry out state estimation on the current measurement value. The state space equation of the particle filter is as follows:
in the formula: h ═ 1000](ii) a The nonlinear state transfer function GP (g) reflects the state X at time kkObtaining a predicted value of the wind speed at the k +1 moment, wherein the function is obtained by training GPR model parameters through a training sample set; wkAnd Vk+1Respectively system process noise and observation noise; x (k))＝[X1(k)X2(k)X3(k)X4(k)]T。
Further, in the step (5), the estimated value and the residual error of the measurement value of the particle filter are analyzed, and the abnormal value is judged and corrected according to a "3 σ" principle, wherein the "3 σ" principle specifically comprises the following steps:
6.1 for test data r1,r2,L,rnTaking the arithmetic mean value thereof
And residual error value
From this, the root mean square deviation is obtained
6.2 the basis for the abnormal value is as follows: if it is
The value is abnormal data; if it is
Then r isiIs normal data.
Has the advantages that: the short-term wind speed prediction method based on the Gaussian process regression and the particle filtering is established, abnormal values existing in an original wind speed sequence are detected and corrected by utilizing the nonlinear and non-Gaussian filtering capabilities of the particle filtering, and meanwhile, the optimal input variable set and the state vector are determined by adopting the partial autocorrelation function, so that the defect of selecting the input variables through manual experience is overcome. The result of the example analysis shows that the wind speed prediction method can realize the online dynamic detection and correction of abnormal values, and establishes a short-term wind speed prediction model for the cleaned time sequence, thereby further enhancing the prediction performance of the model. The method provides an online dynamic detection and correction method for the abnormal value of the wind speed time sequence, improves the short-term wind speed prediction precision, and has certain engineering application significance.
Drawings
FIG. 1 is a graph of autocorrelation and partial autocorrelation functions;
FIG. 2 shows the wind speed fitting results;
FIG. 3 is a partial enlarged view of the wind speed fitting results;
FIG. 4 shows different model fitting residuals;
FIG. 5 shows the wind speed prediction results 15min in advance;
FIG. 6 is a flow chart of the prediction method of the present invention.
Detailed Description
The present invention is further illustrated by the following examples, which are intended to be purely exemplary and are not intended to limit the scope of the invention, as various equivalent modifications of the invention will occur to those skilled in the art upon reading the present disclosure and fall within the scope of the appended claims.
The idea of the invention is to use the nonlinear and non-Gaussian filter characteristics of particle filtering to perform online dynamic detection and correction on abnormal values existing in the original historical wind speed sequence, thereby establishing a wind speed prediction model for the cleaned data and improving the prediction precision. First, to determine the input variable set and the state vector, a partial autocorrelation function is used to measure the correlation between the variables. Secondly, establishing a state space equation through Gaussian process regression in the training sample set, performing state estimation on the current measurement value by adopting a particle filter algorithm, analyzing the residual error of the estimation value and the measurement value, and judging an abnormal value according to a '3 sigma' principle. And then correcting the abnormal value, and reestablishing a Gaussian process regression prediction model for the cleaned wind speed sequence. When wind speed prediction is carried out 15 minutes ahead, the state estimation is carried out on the latest measurement value by adopting a particle filter algorithm, and the online detection and correction of the abnormal value are realized. Finally, the results of example analysis show the effectiveness of the method of the invention.
The method adopts the GPR to establish a short-term wind speed prediction model, the GPR is based on the Bayes theory and the statistical learning theory, and has the advantages of easy programming realization, super-parameter self-adaptive acquisition, output probability distribution and the like when processing complex regression problems such as high dimensionality, small samples, nonlinearity and the like, so that the method is widely applied to multiple fields such as time series analysis, dynamic system model identification, system control and the like.
When applying GPR for short-term wind speed prediction modeling, the training sample set is assumed to be D { (x)i,yi) 1,2,3, ·, n } (X, y), wherein: x is the number ofi∈RmFor an m-dimensional input vector, the m × n-dimensional input matrix can be expressed as X ═ X1,x2,···,xn]N denotes the number of training sample points, yiE R is corresponding to xiIs output scalar. The wind speed prediction process is described by a mathematical language as follows:
defining the function space f (x) ═ Φ (x)Tω，f(x(1))、f(x(2))、…、f(x(n)) A set of random variables is formed, and the Gaussian process model can be expressed as
In the formula: the mean obeying value of the independent white Gaussian noise is 0, and the variance is sigma2Is recorded as ε: N (0, σ)2)；δijFor the function Kroneckerdelta, when i ═ j, the function δ ij1 is ═ 1; m (x) is a mean function of a finite dimension distribution family, and describes a wind speed mean output result; k (x, x') is a covariance function, and the size of the wind speed variance is described.
For simplicity of derivation, the wind velocity mean m (x) is preprocessed to 0. The GPR prediction model establishes a prior distribution in an n-dimensional training set D, n*Dimension test set D*＝{(xi,yi)|i＝n+1,L,n+n*Down-converting into posterior distribution, training sample observation value y and output vector f of test data*Form a joint Gaussian distribution
Wherein K (X, X) ═ KnRepresenting an NxN kernel matrix of elements Kij＝k(xi,xj)；K(X,X*)＝K(X*,X)TFor testing data X*A covariance matrix with the input X of the training set; k (X)*,X*) Is X*Its own covariance.
From this, a prediction value f is derived*The posterior distribution is
Wherein
Mean vector
The mean of the GPR model wind speed predictions, corresponding to the point prediction outputs,
to correspond to
Thereby obtaining the wind speed interval prediction result with the meaning of probability distribution.
The PF algorithm has good nonlinear non-Gaussian system state filtering capability, and random quantity does not need to meet constraint conditions of Gaussian distribution, so that the PF algorithm is applied to the fields of signal processing, communication, artificial intelligence and the like. The method selects a particle filter algorithm to process abnormal values existing in the wind speed sequence, and provides a short-term wind speed prediction model based on GPR-PF.
The basic idea of PF is to approximate the posterior probability distribution of a system with a set of particles and then estimate the state of a non-linear system with this approximate representation. The particle filtering process is described by a nonlinear system dynamic state space model as
In the formula: x is the number ofkAnd zkRespectively is a system state vector and a measurement value at the k moment; f (g) and h (g) are the system state transfer function and the measurement model function, respectively; w is ak-1V and vkRespectively system process noise and observation noise; from the importance density function q (x)k|x1:k-1,zk) Sampling N samples and expressing these samples as:
the predicted value at state k is
Namely, it is
In the formula:
is an independent sample corresponding to particle i sampled in the known noise profile of the system. All particles that complete the prediction phase constitute a prior probability sample at time k, denoted
That is, the prior probability density p (x) is obtainedk|Zk-1). After obtaining a new observed quantity zkThen, each particle
Updating according to weight formula
Normalizing the weight
And (3) overcoming the particle degradation phenomenon by utilizing a resampling method. Resampling the sample according to each particle normalized weight value, copying the particles with larger weight values, deleting the particles with smaller weight values to obtain an equal-weight-value particle set, and obtaining a posterior distribution density function
In the formula: δ (g) is the dirac Kronecker delta function and a loop iteration process ends.
The optimum state in the sense of the minimum mean square error criterion is estimated as
The autocorrelation function and the partial autocorrelation function have important significance in the process of identifying the model type and estimating the order. The invention measures X based on autocorrelation function and partial autocorrelation functionkAnd Xk-τThe time delay is effectively analyzed, and the input variable set and the state vector are determined. Where τ is the delay time.
Measured wind speed (data sampling time interval is 15min) of a certain wind power plant in Jiangsu province is used for GPR-PF short-term wind speed prediction modeling, and FIG. 1 is an autocorrelation function graph and a partial autocorrelation function graph of time series analysis. It can be seen from the figure that the autocorrelation function has a tail-off characteristic, while the partial autocorrelation function is truncated, so that the wind velocity sequence satisfies the AR model. Combining a partial autocorrelation function graph, selecting 4 input variables, namely predicting the wind speed X at the k +1 momentk+1Then, the wind speed X at the moment k, k-1, k-2, k-3 is measuredk,Xk-1,Xk-2,Xk-3As input variables. Let X1(k)＝X(k)，X2(k)＝X(k-1)，X3(k)＝X(k-2)，X4(k) X (k-3), the state vector at time k is X (k) ═ X1(k)X2(k)X3(k)X4(k)]T。
When the particle filtering is adopted to detect and correct the wind speed sequence abnormal value, the historical wind speed value is firstly adopted to predict the wind speed state at the current moment, and then the predicted value is corrected according to the wind speed measured value at the current moment, so that the optimal estimation of the measured value at the moment is obtained, and the residual error between the wind speed estimated value and the measured value is obtained.
In combination with the state vector determined by the partial autocorrelation function, the GPR-PF short-term wind speed prediction state space model of the invention is as follows:
in the formula: h ═ 1000](ii) a The nonlinear state transfer function GP (g) reflects the state X at time kkAnd obtaining a predicted value of the wind speed at the k +1 moment, wherein the function is obtained by training GPR model parameters through a training sample set.
The particle filter estimates the state of the moment k to obtain an estimated value of the wind speed at the moment k +1, and corrects the estimated value according to the measured value at the moment k +1, so that the optimal estimated value of the wind speed after filtering is obtained.
The method adopts a deviation-based data abnormal value detection method to detect and correct an abnormal value existing in an original wind speed sequence, and judges the abnormal value according to a '3 sigma' criterion by analyzing a residual r existing between a GPR-PF wind speed estimation value and a measurement value.
For test data r1,r2,L,rnTaking the arithmetic mean value thereof
And residual error value
From this, the root mean square deviation is obtained
The basis for the abnormal value is as follows: if it is
The value is abnormal data; if it is
Then r isiIs normal data.
In order to quantify the degree that the predicted value approaches the true value, the average absolute percentage error (MAPE) and the Root Mean Square Error (RMSE) are selected as the evaluation indexes of the model prediction effect, and the calculation formulas are respectively as follows:
in the formula: t is the number of predicted points, yiFor the true value of the wind speed at the ith prediction point,
and predicting the model predicted value of the ith prediction point.
According to the method, 1104 actual measurement wind speed values from 2008, 14, 12:00 days to 5, 25, 23:45 days in a certain wind power plant are used as training sample sequences, the data sampling time interval is 15min, a GPR-PF wind speed prediction model is established, and 96 wind speed values from 5, 26 days in a certain wind power plant are predicted in advance by one step (namely, 15min in advance).
Firstly, a GPR short-term wind speed prediction model is established by a training sample set, model hyperparameters are solved, a state space equation is established, and residual errors between model fitting values and measurement values are analyzed, so that abnormal value detection is performed by a deviation-based method. FIG. 2 shows the prediction results obtained by using GPR and GPR-PF methods in the training process. It can be seen from the figure that, when the GPR model is used for short-term wind speed prediction, the GPR model is difficult to track the wind speed variation trend well due to strong fluctuation and randomness of the wind speed, and has a certain hysteresis, thereby generating a large deviation. The GPR-PF model dynamically updates the wind speed estimation value by adopting the current moment measurement value, and can well estimate the real state of the wind speed. The partial enlargement of the prediction from fig. 3 allows a more detailed comparison of the fit of the two models. Residual analysis is performed on the predicted wind speed value and the actual measurement value, and fig. 4 shows the residual results when the GPR model and the GPR-PF model are adopted for fitting respectively. When the GPR model is singly adopted, the fact that residual distribution is scattered is seen, and analysis and detection of abnormal values are not facilitated. When the GPR-PF mixing method is adopted, residual distribution is concentrated, and abnormal values can be judged easily by adopting a '3 sigma' criterion.
The results of the outlier detection and correction by analysis of the residual distribution and the "3 σ" criterion are shown in table 1.
TABLE 1 results of abnormal value detection and correction
And (4) re-establishing a GPR prediction model for the cleaned wind speed sequence, and predicting the short-term wind speed 15min in advance. FIG. 5 shows the wind speed prediction results of the BP neural network, the SVM, the GPR and the GPR-PF models. The results of quantitative evaluation indexes of the prediction model are shown in table 2. It can be seen that the GPR can provide better prediction accuracy compared with two prediction models, namely a BP neural network and an SVM. After the abnormal value is corrected by adopting a particle filter algorithm, the GPR-PF wind speed prediction model weakens the noise influence, so that the optimal prediction result is obtained.
TABLE 2 wind speed prediction error 15min ahead
In summary, the short-term wind speed prediction method based on the gaussian process regression and the particle filter has the following advantages: 1) the bias autocorrelation function is adopted to select the input variable set and determine the state vector, thereby avoiding the deficiency of manual experience in selecting the input variables. 2) And establishing a state space equation based on particle filtering, realizing online dynamic detection and correction of abnormal values in the historical wind speed sequence, and establishing a Gaussian process regression short-term wind speed prediction model for the cleaned wind speed time sequence, thereby further improving the prediction precision. 3) Compared with a support vector machine and a BP neural network prediction method, the method adopts the Gaussian process regression to establish the short-term wind speed prediction model, has better prediction performance, and the super-parameters of the model can be acquired in a self-adaptive manner. The method can carry out on-line dynamic detection and correction on the abnormal value existing in the original time sequence, thereby improving the short-term wind speed prediction precision and having certain reference value for arranging a wind power output plan for the power system and ensuring the safe and stable operation of the power grid.
Claims (6)
1. A short-term wind speed prediction method based on Gaussian process regression and particle filtering is characterized by comprising the following steps: the method comprises the following steps:
(1) acquiring basic data required by short-term wind speed prediction of a power system, and carrying out zero-averaging processing on an original wind speed time sequence;
(2) determining an input variable set with the maximum correlation with the wind speed value at the moment to be predicted by adopting a partial autocorrelation function, determining a state vector and constructing a training sample set by using a historical measured wind speed value;
(3) establishing a Gaussian process regression short-term wind speed prediction model in a training sample set, and giving a training process fitting residual error;
(4) establishing a particle filter state space equation by combining the state vector and a Gaussian process regression model, and performing state estimation on the current measurement value by adopting a particle filter algorithm;
(5) analyzing the estimated value and the residual error of the measured value of the particle filter, and judging and correcting an abnormal value according to a '3 sigma' principle;
(6) and (3) re-establishing a Gaussian process regression prediction model for the cleaned wind speed sequence, and performing state estimation on the latest measurement value by adopting a particle filter algorithm when wind speed prediction is performed for 15 minutes in advance, so as to realize online detection and correction of the abnormal value.
2. The method for short-term wind speed prediction using gaussian process regression and particle filtering as defined in claim 1, wherein: in the step (1), zero-averaging processing is performed on the original wind speed time sequence, wherein a zero-averaging formula is as follows:
in the formula: x (t) is the time series of the original wind speeds,
is the average value of the sequence x (t).
3. The method for short-term wind speed prediction using gaussian process regression and particle filtering as defined in claim 1, wherein: determining an input variable set with maximum correlation with the wind speed value at the moment to be predicted by adopting a partial autocorrelation function, determining a state vector and constructing a proper training sample set, wherein the calculation method of the partial autocorrelation function comprises the following steps:
3.1 hypothesis xiIs an output variable, and when the lag order is k, the value of the partial autocorrelation coefficient is in a 95% confidence interval
Inner, then xi-kCan be used as one of the input vectors, if all the partial autocorrelation coefficient values are within the 95% confidence interval, then x is considered to bei-1Is an input variable;
3.2 for time series { x1,x2,L,xnThe covariance of lag order k is defined as gammakThe calculation formula is as follows:
in the formula: k is 0,1,2, L, M,
is the mean of the time series; m-n/4 is the maximum hysteresis order;
3.3 the autocorrelation function with a lag order k is defined as ρk：
In the formula:
the covariance when the hysteresis order k is 0;
the PACF for a lag order of k is defined as αkk：
In the formula: k is 1,2, L, M.
4. The method for short-term wind speed prediction using gaussian process regression and particle filtering as defined in claim 1, wherein: step (3) establishing a Gaussian process regression short-term wind speed prediction model in the training sample set, and giving a fitting residual error of the training process, wherein the prediction process of the Gaussian process regression model is as follows:
4.1 assume that the training set is D { (x)i,yi) 1,2,3, …, n } ═ X, y, where: x is the number ofi∈RmFor an m-dimensional input vector, the m × n-dimensional input matrix can be expressed as X ═ X1,x2,…,xn]N denotes the number of training sample points, yiE R is corresponding to xiAn output scalar of (1);
4.2 define the function space f (x) ═ Φ (x)Tω，f(x(1))、f(x(2))、…、f(x(n)) Forming a set of random variables and following a joint gaussian distribution, the gaussian process model can be expressed as:
in the formula: the mean obeying value of the independent white Gaussian noise is 0, and the variance is sigma2Is recorded as ε: N (0, σ)2)；δijIs a Kronecker delta function, when i is equal to j, the function deltaij1 is ═ 1; m (x) is a mean function of a finite dimension distribution family, and describes a wind speed mean output result; k (x, x') is a covariance function and describes the size of the wind speed variance;
4.3GPR prediction model establishes prior distributions in n-dimensional training set D, n*Dimension test set D*＝{(xi,yi)|i＝n+1,L,n+n*Down-converting into posterior distribution, training sample observation value y and output vector f of test data*Form a joint Gaussian distribution
Wherein K (X, X) ═ KnRepresenting an NxN kernel matrix of which element Kij＝k(xi,xj)；K(X,X*)＝K(X*,X)TFor testing data X*A covariance matrix with the input X of the training set; k (X)*,X*) Is X*(ii) its own covariance;
4.4 deriving therefrom the predicted value f*The posterior distribution is
Wherein
Mean vector
The mean of the GPR model wind speed predictions, corresponding to the point prediction outputs,
to correspond to
Thereby obtaining the wind speed interval prediction result with the meaning of probability distribution.
5. The method for short-term wind speed prediction using gaussian process regression and particle filtering as defined in claim 1, wherein: and (4) establishing a particle filter state space equation by combining the state vector and a Gaussian process regression model, and performing state estimation on the current measurement value by adopting a particle filter algorithm, wherein the particle filter state space equation is as follows:
in the formula: h ═ 1000](ii) a The nonlinear state transfer function GP (g) reflects the state X at time kkObtaining a predicted value of the wind speed at the k +1 moment, wherein the function is obtained by training GPR model parameters through a training set; wkAnd Vk+1Respectively system process noise and observation noise; x (k) ═ X1(k) X2(k) X3(k) X4(k)]T。
6. The method for short-term wind speed prediction using gaussian process regression and particle filtering as defined in claim 1, wherein: analyzing the estimated value and the measurement value residual error of the particle filter in the step (5), and judging and correcting an abnormal value according to a '3 sigma' principle, wherein the '3 sigma' principle comprises the following specific processes:
6.1 for test data r1,r2,L,rnTaking the arithmetic mean value thereof
And residual error value
From this, the root mean square deviation is obtained
6.2 the basis for the abnormal value is as follows: if it is
riIs abnormal data; if it is
Then r isiIs normal data.
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